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2 Answers
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“Are they used?” and “Are they acceptable?” are different questions. The regular forms such as お借りします and お食べになります are used, but they are less formal than the irregular forms such as 拝借します and 召し上がります. Whether the less formal expressions are acceptable or not depends on how formally you want to speak.

By the way, you are confusing grammatical terms “respectful form,” “humble form,” “polite form,” and “honorific form.” 拝借します is the polite form of the humble form of 借りる, where the humble form of 借りる is 拝借する. 召し上がります is the polite form of the respectful form of 食べる, where the respectful form of 食べる is 召し上がる. Whether an expression is in polite form or not is orthogonal to whether it is in respectful or humble form. Honorifics are the broader concept which includes all of respectful form, humble form, and polite form. For details, see Wikipedia.

@Pacerier It appears to me that it's not working <@_@>. In the head of the form, 「見出し語」＝vocabulary entry, 「尊敬語」＝respectful form, 「謙譲語」＝humble form, 「丁寧語」＝polite form. As to the polite forms, I agree with Ito-san's opinion: "Whether an expression is in polite form or not is orthogonal to whether it is in respectful or humble form.". So I think it's not very appropriate for the page to give "polite forms" a column there.
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NoirMay 22 '14 at 11:32